I haven’t had this long. I used a fish inverter for a project I’m working on. Everything worked great until one channel broke so it’s always on. Then another channel broke so it’s always off. This sucks because I was originally planning on using all 8 channels and now I’m down to 6. It seems like the TRIACs are capable of handling a voltage higher than the recommended inverter’s output.

I think tying logic GND and HVGND might cause a major problem for you. I’m pretty sure the reason you can’t have more than 2 on at any given time is that 3 or more on at once be too much for the driver and you won’t get good/noticeable lighting on your EL wire.
The TRIAC looks like it’s voltage controlled, kind of like a MOSFET, so there’s no need for there to be a GND coming from the Arduino pin because there is almost no current actually drawn (there will always be some tiny amount, but in this case it’s negligible.)
If you want to drive more than 2 wires, but not all of them at once, write something in software that looks like the “all_on” function, but limit it to the number of wires you want.

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